Question

I have this worksheet, it has a bunch of different kinds of questions, but i know all the stuff we learned, i just don't know which ones i use. 1) factor each expression, 8x+10 2) Use Foil to factor each expression, x2-5x+6 3) Use foil to factor each expression, n2+n-20.

Answer 1

8 x + 10
all you can do here is factor out 2
= 2 (4x+5)

x^2 - 5 x + 6
is quadratic and of form a x^2 + b x + c
we know it will have factors of form ( p x + q)(r x + s) which we can foil to get the original back (We do not know however if all those constants are integers, but we can hope
Now 6 is either 6*1 or it is 2 * 3
we know p and r are one to get 1 x^2
we know both q and s must be - to get a positive outer product and negative inner product so
so try to FOIL
(x-2)(x-3) (by the way it works)

n^2 + n - 20
well, 20 = 2 * 10 or 20*1 or 4*5
I know I need
(n - something ) (n + something that is one bigger and gives an outer product of 20
so try to FOIL
(n-4)(n+5)